Move LimitPushdown to physical-optimizer crate (#11945)

* Move LimitPushdown to physical-optimizer crate

* Add comment about test code location

* asf header

* Fix clippy

---------

Co-authored-by: Andrew Lamb <[email protected]>

Author: lewiszlw

datafusion/common/src/utils/mod.rs

@@ -37,7 +37,7 @@ use sqlparser::ast::Ident;
 use sqlparser::dialect::GenericDialect;
 use sqlparser::parser::Parser;
 use std::borrow::{Borrow, Cow};
-use std::cmp::Ordering;
+use std::cmp::{min, Ordering};
 use std::collections::HashSet;
 use std::ops::Range;
 use std::sync::Arc;
@@ -683,6 +683,69 @@ pub fn transpose<T>(original: Vec<Vec<T>>) -> Vec<Vec<T>> {
     }
 }
 
+/// Computes the `skip` and `fetch` parameters of a single limit that would be
+/// equivalent to two consecutive limits with the given `skip`/`fetch` parameters.
+///
+/// There are multiple cases to consider:
+///
+/// # Case 0: Parent and child are disjoint (`child_fetch <= skip`).
+///
+/// ```text
+///   Before merging:
+///                     |........skip........|---fetch-->|     Parent limit
+///    |...child_skip...|---child_fetch-->|                    Child limit
+/// ```
+///
+///   After merging:
+/// ```text
+///    |.........(child_skip + skip).........|
+/// ```
+///
+/// # Case 1: Parent is beyond child's range (`skip < child_fetch <= skip + fetch`).
+///
+///   Before merging:
+/// ```text
+///                     |...skip...|------------fetch------------>|   Parent limit
+///    |...child_skip...|-------------child_fetch------------>|       Child limit
+/// ```
+///
+///   After merging:
+/// ```text
+///    |....(child_skip + skip)....|---(child_fetch - skip)-->|
+/// ```
+///
+///  # Case 2: Parent is within child's range (`skip + fetch < child_fetch`).
+///
+///   Before merging:
+/// ```text
+///                     |...skip...|---fetch-->|                   Parent limit
+///    |...child_skip...|-------------child_fetch------------>|    Child limit
+/// ```
+///
+///   After merging:
+/// ```text
+///    |....(child_skip + skip)....|---fetch-->|
+/// ```
+pub fn combine_limit(
+    parent_skip: usize,
+    parent_fetch: Option<usize>,
+    child_skip: usize,
+    child_fetch: Option<usize>,
+) -> (usize, Option<usize>) {
+    let combined_skip = child_skip.saturating_add(parent_skip);
+
+    let combined_fetch = match (parent_fetch, child_fetch) {
+        (Some(parent_fetch), Some(child_fetch)) => {
+            Some(min(parent_fetch, child_fetch.saturating_sub(parent_skip)))
+        }
+        (Some(parent_fetch), None) => Some(parent_fetch),
+        (None, Some(child_fetch)) => Some(child_fetch.saturating_sub(parent_skip)),
+        (None, None) => None,
+    };
+
+    (combined_skip, combined_fetch)
+}
+
 #[cfg(test)]
 mod tests {
     use crate::ScalarValue::Null;